Numerical integration of Heath-Jarrow-Morton model of interest rates

We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM) model. To construct the methods, we first discretize the infinite dimensional HJM equation in maturity time variable using quadrature rules for approximating the arbitrage-free drift. This results in a finite dimensional system of stochastic differential equations (SDEs) which we approximate in the weak and mean-square sense using the general theory of numerical integration of SDEs. The proposed numerical algorithms are computationally highly efficient due to the use of high-order quadrature rules which allow us to take relatively large discretization steps in the maturity time without affecting overall accuracy of the algorithms. Convergence theorems for the methods are proved. Results of some numerical experiments with European-type interest rate derivatives are presented.Comment: 48 page

Competing ideologies of Russia's civil society

Many analysts and public opinion makers in the West conflate the notions of Russia’s non-systemic liberal opposition and the country’s civil society. Indeed, despite garnering the support of a minority of Russia’s population, non-systemic liberal opposition represents a well-organized civic group with a clearly articulated agenda and the ability to take action. Yet, does Russia’s civil society end there? A closer look at the country’s politics shows that Russia has a substantial conservative-traditionalist faction that has also developed agenda for action and formulated opinions. This group is anti-liberal rather than illiberal ideologically and pro-strong state/pro a geopolitically independent Russia rather than pro-Kremlin politically. The interaction between liberal and conservative civic groups represents the battle of meanings, ideas, and ethics, and ultimately determines the future trajectory of Russia’s evolution. Thus, the analysis of Russia’s civil society must represent a rather more nuanced picture than a mere study of the liberal non-systemic opposition. This article will examine the complexity of Russia’s civil society scene with reference to the interplay between the liberal opposition and conservative majority factions. The paper will argue that such complexity stems from ideological value pluralism that falls far beyond the boundaries of the liberal consensus, often skewing our understanding of political practice in Russia

Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state

In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of regular and random grids and explain recently observed dramatic differences in resonance broadening in the electric and magnetic modes of random arrays. We show that randomness in the particle positioning influences equally on the scattering loss from both electric and magnetic dipoles, however, the observed resonance broadening can be very different depending on the absorption level in different modes as well as on the average electrical distance between the particles. The theory is illustrated by an example of a planar metasurface composed of cut-wire pairs. We show that in this particular case at the magnetic resonance the array response is almost not affected by positioning randomness due to lower frequency and higher absorption losses in that mode. The developed model allows predictions of behavior of random grids based on the knowledge of polarizabilities of single inclusions.Comment: 13 pages, 5 figures, and submitted to PR

Shadow-free multimers as extreme-performance meta-atoms

We generalize the concept of parity-time symmetric structures with the goal to create meta-atoms exhibiting extraordinary abilities to overcome the presumed limitations in the scattering of overall lossless particles, such as non-zero forward scattering and the equality of scattering and extinction powers for all lossless particles. Although the forward scattering amplitude and the extinction cross section of our proposed meta-atoms vanish, they scatter incident energy into other directions, with controllable directionality. These meta-atoms possess extreme electromagnetic properties not achievable for passive scatterers. As an example, we study meta-atoms consisting of two or three small dipole scatters. We consider possible microwave realizations in the form of short dipole antennas loaded by lumped elements. The proposed meta-atom empowers extraordinary response of a shadow-free scatterer and theoretically enables most unusual material properties when used as a building block of an artificial medium.Comment: 14 pages, 9 Figure